source of earnings

Source of Earnings Thomas Hinton, FCIA, FSA

With assistance from Blake A. Hill, FCIA, FSA

CIA Practice Education Course – Finance/Investment and Individual Life and Annuities

Background

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Classic Financial Statements: Point in Time: Balance Sheets

Change over Time Income Statements Source of Earnings

Background

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Income Statements: Revenue Premium Investment Income

Less Dispositions Expenses Claims Change in Reserves …

= Net Income Before Tax

Background

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So what value does an SOE analysis provide over a traditional Income Statement?

Example: What happened here?

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Actual Plan Premium 1,000 900 Investment Income 100 110 Claims 500 400 Surrenders 200 160 Change in Reserves 300 300 Net Income Before Tax 100 150

Background

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SOE analysis should be: Consistent with other reporting; Easy to understand, produce, and replicate; Well documented; Contain all components of earnings/explain material aspects of

net income.

Components of an SOE

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Expected Earnings on In-force (EEOI) Impact of New Business Experience Gains/Losses Changes in Assumptions Other Income on Surplus Taxes

EEOI

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Earnings that would be reflected if actual results matched valuation best estimate.

Includes Expected release of PfAD Expected Fee Income Income from Funds on Deposit Amortization of Balance Sheet Amounts

Impact of New Business

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Gain/Strain from NB written = PV(Profit) – PfAD = - Time Zero Reserve

Note impact of differences between pricing and valuation

assumptions!

Experience G/L

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Actual experience vs valuation best estimate over the reporting period. Mortality/Morbidity Surrender Investment and so on …

Experience G/L

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Why can’t we just take Actual/Expected from plan or budget?

Hint: what Income Statement Lines are impacted by variances in: New Business Mortality Experience Lapse …

Changes in Assumptions and Other

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Best estimate assumptions and margins; Changes in methodology; Correction of errors; Management actions.

Income on Surplus Taxes

Sample Report

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Expected Profit on In-force Operations x,xxx x,xxx Impact of New Business xxx xxx Experience Gains & Losses xxx xxx Changes in Best Estimate Assumptions and Other Changes xxx xxx Earnings on Operations Before Taxes xxx xxx Earnings on Surplus xxx xxx Net Income Before Taxes x,xxx x,xxx Less: Taxes xxx xxx Net Income Before Minority Interests xxx xxx Less: Minority Interests xxx xxx Net Income xxx xxx

Other Considerations

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Need to be able to differentiate PfAD from best estimate reserve.

Approximations may be required to determine CALM reserve associated with NB.

Order may matter in calculation due to inter-relationships.

Par Business Key is to explain items that effect net income. Experience passed through dividends would not be included.

Data used would be consistent with ledger and existing processes.

Example: Question 3 from 2010 Exam

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Policy 1 Policy 2

Face Amount $100,000 $50,000

Maturity Date Dec 31, 2011 Dec 31, 2012

Premium payable BOY $1,500 $600

Date of Birth Dec 31, 1939 Dec 31, 1938

As valuation actuary at SimplyLife Co, you are responsible for preparing the financial statements for the life insurance business unit. The business unit is closed to new business and at December 31, 2009 consists of two policies, both Non-Renewable 5-Year Term Insurance. Your business unit is not responsible for surplus management.

Example: Question 3

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Balance Sheet: Dec 31, 2009 Assets $5,420 Policy 1 Best-Estimate $2,153 Policy 1 PfAD $500 Policy 2 Best-Estimate $2,372 Policy 2 PfAD $395 Total Liabilities $5,420

Example: Question 3

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Valuation assumptions: Mortality MfAD is 10% of best estimate q(71) = 0.027 q(72) = 0.028 q(73) = 0.030 q(74) = 0.034 Valuation Interest Rate = 5%

Example: Question 3

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Assume: No Taxes No Expenses

Experience: Assets Earned 7% in 2010 Policy 1 died Dec 31, 2010

Example: Solution

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Please note: the solution that follows is not the only correct answer to the question! There are many equally correct ways to solve the question and receive full marks.

A less ambiguous (and much easier to grade) question would have provided PfADed and Best-Estimate Reserves rather than have candidates calculate them.

Example: Solution to Part A

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Part A – Construct the 2010 Income Statement: Premium Income Both policies pay premiums at the beginning of each year: $1,500 + $600 = $2,100

Investment Income Actual Assets * Actual rate of return ($5,420 + $1,500 + $600) * 7% = $526

Claims Policy 1 dies: $100,000.

Change in Reserves Closing Reserve – Opening Reserve = ($0 + Policy 2 PfADed Rsv @2010/12/31) – $5,420 = $2,059 – $5,420 = -$3,361


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Policy 2 was born Dec 31, 1938. On Dec 31, 2011, life turned 73 years old. Policy could have died on Dec 31, 2011 and 2012 before policy expires on Dec 31, 2012.

Policy 2 PfADed Rsv @ 2010/12/31: = PV (DB) – PV (Premium) = $50,000 * ( ( q(73) * 1.1 ) / (1+i) + (1 – ( q(73) * 1.1 ) ) * ( q(74) * 1.1 ) / (1+i)^2 ) - $600 * ( 1 + (1 – ( q(73) * 1.1) ) / (1+i) ) = $3,211.60 – $1,152.57 = $2,059


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While we’re here, calculate the best estimate reserve and PfADs for Pol. 2:

Policy 2 B/E Rsv @ 2010/12/31: = PV (DB) – PV (Premium) = $50,000 * ( q(73) / (1+i) + (1 – q(73) ) * q(74) ) / (1+i)^2 ) - $600 * ( 1 + (1 – q(73) ) / (1+i) ) = $2,924.26 – $1,154.29 = $1,770 PfADs = PfADed Rsv – B/E Rsv = $2,059 – $1,770 = $289


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While we’re here, calculate the PfADed and B/E Reserves for Policy 1: Policy 1 PfADed Rsv @ 2010/12/31:

= $100,000 * (q(72) * 1.1 / (1+i)) - $1,500 * ( 1 ) = $2,933 – $1,500 = $1,433

Policy 1 B/E Rsv @ 2010/12/31:

= $100,000 * (q(72) / (1+i)) - $1,500 * ( 1 ) = $2,667 – $1,500 = $1,167

PfADs = PfADed Rsv – B/E Rsv = $1,433 – $1,167 = $267

Example: Summary

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Policy 1 Best-Est PfAD Total 2009/12/31 $2,153 $500 $2,653 2010/12/31 $1,167 $267 $1,433 Policy 2 Best-Est PfAD Total 2009/12/31 $2,372 $395 $2,767 2010/12/31 $1,770 $289 $2,059


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Income Statement Premium $2,100 Investment Income $526 Revenue $2,626 Benefits $100,000 Change in Reserves -$3,361 Dispositions $96,639 Net Income -$94,013

Example: Additional Question

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Exercise: Construct the best estimate Income Statement: Premium Income

= $1,500 + $600 = $2,100

Investment Income = ($5,420 + $1,500 + $600) * 5% = $376

Expected Claims = 0.027 * $100,000 + 0.028 * $50,000 = $4,100

Expected Change in Reserves

= ((0.973 * $1,433) + (0.972 * $2,059)) - $5,420 = $3,396 - $5,420 = -$2,024

Example: Additional Question

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B/E Income Statement Premium $2,100 Investment Income $376 Revenue $2,476 Benefits $4,100 Change in Reserves -$2,024 Dispositions $2,076 Net Income $400

Example: Homework Questions

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What does the Income Statement look like if: Policy 1 survives but Policy 2 dies on Dec 31, 2010? Both Policies survive? Both Policies die on Dec 31, 2010? How would these income statements reflect lapses?

Example: Solution to Part B

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Part B – Create an SOE Expected change in PfADs: = Rsv(0) - [ tPx * Rsv(1) ] = ($500 + $395) - ((0.973 * $267) + (0.972 * $289)) = $895 - $540 = $355 Interest on PfADs: = ($500 + $395) * 5% = $45 Expected Earnings on In-Force: = Expected PfAD Release + Interest on PfADs = $355 + $45 = $400 Question: Where have we seen this $400 before?


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Investment Experience Gain/Loss = Actual Investment Income – Expected Investment Income = ($5,420 + $1,500 + $600) * (0.07 – 0.05) = $150 Mortality Experience Gain/Loss = (Expected Benefits – Expected Reserve Release) – (Actual Benefits - Actual Reserve Release) Expected Benefits = (0.027 * $100,000) + (0.028 * $50,000) = $2,700 + $1,400 = $4,100 Actual Benefits = $100,000


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Expected Reserve Release = qx(b/e) * B/E Rsv at End of Period = (0.027 * $1,167) + (0.28 * $1,770) = $81 Actual Reserve Release = (1 * $1,167) + (0 * $1,770) = $1,167 Mortality Gain / Loss = ($4,100 – $81) – ($100,000 – $1,167) = -$94,814


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Gain/Loss in PfADs: = Expected PfADs - Actual PfADs = ((0.973 * $267) + (0.972 * $289)) - ((0 * $267) + (1 * $289)) = $541 - $289 = $252 Note: if we had used reserves with PfADs (and not best estimate reserves) in the calculation of Mortality Gain/Loss there would be no outstanding G/L on PfADs. Question: what would be the rationale for aggregating all the PfAD G/L as one item rather than embedding them in the respective source? Question: why would some want to report G/L on PfADs separately? What is different between PfADs and Best-Estimate Reserves?


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SOE Report Expected Profit on In-force Operations $400 Impact of New Business $0 Investment $150 Mortality -$94,814 PfAD $252 Experience Gains & Losses -$94,412 Unexplained $0 Net Income -$94,012


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SOE (CIA Sample) Expected Profit on In-force Operations $400 Impact of New Business $0 Experience Gains & Losses -$94,412 Changes in Best Estimate Assumptions and Other Changes $0 Earnings on Operations Before Taxes -$94,012 Earnings on Surplus $0 Net Income Before Taxes $0 Less: Taxes $0 Net Income Before Minority Interests -$94,012 Less: Minority Interests $0 Net Income -$94,012

Example: Additional Exercise

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What would our Best-Estimate Income Statement look like if we split out Expected Earnings on In-force from Revenues and Dispositions?

That is: take the Income Statement from Page 25 and morph it into a Source of Earnings Statement.


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Income Statement (from page 25) Premium $2,100 Investment Income $376 Revenue $2,476 Benefits $4,100 Change in Reserves -$2,024 Dispositions $2,076 Net Income $400


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From page 28: Expected Earnings on In-Force:

= Expected PfAD Release + Interest on PfADs = $355 + $45 = $400

Change in Reserves + Expected PfAD Release (Watch the signs!)

= -$2,024 + $355 = -$1,669

Investment Income – Interest on PfADs = $376 - $45 = $331


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Premium $2,100 Best-Est $331 PfAD $45 Investment Income $376 Revenue $2,476 Benefits $4,100 Best-Est -$1,669 PfAD -$355 Change in Reserves -$2,024 Dispositions $2,076 Net Income $400


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B/E Income Statement with EEOI broken out: Interest on PfADs $45 Change in PfADs $355 (subtracting a negative!) Expected Earnings on In-force $400 Premium $2,100 Investment Income (B/E) $331 Revenue $2,431 Benefits $4,100 Change in B/E Reserves -$1,669 Dispositions $2,431 Net Income $400


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More like an SOE: Interest on PfADs $45 Change in PfADs $355 Expected Earnings on In-force $400 Premium $2,100 Investment Income (B/E) $331 Benefits -$4,100 Change in B/E Reserves $1,669 Other $0 Net Income $400

Example: a different perspective

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So where did all the change in reserves go in the SOE? Income Statement Opening Closing Change PfADs $896 $289 -$607 Best Estimate $4,524 $1,770 -$2,754 Total Reserve $5,420 $2,059 -$3,341

Source of Earnings Opening Closing Change Expected Change in B/E Rsv $4,524 $2,856 -$1,669 Mortality G/L (Rsv only) - ($81 - $1,167) -$1,086 Best Estimate Rsv $4,524 $1,770 -$2,754 EEOI (PfAD Rsv only) $896 $541 -$355 PfAD G/L - -$252 -$252 PfADs $896 $289 -$607 Question: where does the “Expected Change in Reserves” appear in the SOE calculation? Hint: $1,669 + $355 = $2,024

Example: More Homework

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Build Source of Earnings to match the Income Statements you calculated for the homework on page 28.

source of earnings

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